Hi Pamela. I researched the same records as appear on the Charles City County site (to 1837) and did not find anything on William Fields, born about 1829.

However, I think you could make a good argument for descent from the Charles City County Fields if you could find the evidence that the Connecticut Fields came from Virginia. Their Charles City County registrations indicate the the family was very light-skinned, so that would provide another clue.
Paul